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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 16 Aug 2010 14:46:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/16/t1281969945wc6137v3rkb7nhd.htm/, Retrieved Thu, 16 May 2024 22:21:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79008, Retrieved Thu, 16 May 2024 22:21:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten] [2010-08-16 14:46:23] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
257
256
255
253
251
250
251
253
254
254
255
257
260
251
255
252
245
239
240
247
251
255
259
260
259
266
261
243
232
225
229
238
240
241
239
246
242
251
246
219
203
192
197
203
208
207
208
212
208
215
200
170
162
150
148
152
155
150
146
147
142
146
130
102
98
90
86
104
108
94
88
92
93
95
81
50
49
34
27
45
47
42
32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79008&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79008&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79008&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean186.0843373493988.150350410796522.8314523879731
Geometric Mean163.823684646856
Harmonic Mean131.955614287802
Quadratic Mean200.186148311774
Winsorized Mean ( 1 / 27 )186.0843373493988.1292310544881522.8907674172529
Winsorized Mean ( 2 / 27 )186.108433734948.115461458086922.9325756392431
Winsorized Mean ( 3 / 27 )186.3975903614468.0507853895802723.1527212988053
Winsorized Mean ( 4 / 27 )186.4939759036148.0140629682012423.2708398528435
Winsorized Mean ( 5 / 27 )186.6144578313257.9882523083160623.3611121217407
Winsorized Mean ( 6 / 27 )186.6144578313257.9417662943098223.4978531117231
Winsorized Mean ( 7 / 27 )186.6987951807237.9239838164826323.5612287335029
Winsorized Mean ( 8 / 27 )189.5903614457837.3274055180795125.874146173293
Winsorized Mean ( 9 / 27 )190.0240963855427.2188202109221526.3234283211589
Winsorized Mean ( 10 / 27 )190.2650602409647.1767100613400826.5114597935194
Winsorized Mean ( 11 / 27 )190.5301204819287.1308936082711526.7189683297099
Winsorized Mean ( 12 / 27 )190.8192771084347.08143190374126.9464254831889
Winsorized Mean ( 13 / 27 )190.8192771084347.037599882104127.1142549029631
Winsorized Mean ( 14 / 27 )190.9879518072297.0090721190886527.2486783645853
Winsorized Mean ( 15 / 27 )190.9879518072296.958896448528427.4451492732899
Winsorized Mean ( 16 / 27 )191.5662650602416.8621709093345227.9162771652417
Winsorized Mean ( 17 / 27 )192.1807228915666.7045264024404228.6643248688846
Winsorized Mean ( 18 / 27 )192.3975903614466.6100605376355429.1067818919352
Winsorized Mean ( 19 / 27 )193.3132530120486.4616667922912829.9169330802804
Winsorized Mean ( 20 / 27 )198.6144578313255.6393164389584835.2195979745388
Winsorized Mean ( 21 / 27 )201.6506024096395.2012237120822438.7698383250103
Winsorized Mean ( 22 / 27 )202.7108433734945.0545228876957140.1048423120124
Winsorized Mean ( 23 / 27 )202.4337349397595.0223769846837540.3063600277521
Winsorized Mean ( 24 / 27 )201.8554216867474.8837539614958941.3320210801362
Winsorized Mean ( 25 / 27 )201.8554216867474.8087163895116241.9769862342095
Winsorized Mean ( 26 / 27 )202.4819277108434.7234841184650442.8670707114905
Winsorized Mean ( 27 / 27 )202.1566265060244.6870778502109343.1306312731559
Trimmed Mean ( 1 / 27 )187.0617283950628.0540103054127723.2259112295082
Trimmed Mean ( 2 / 27 )188.0886075949377.9631614882021123.61984092293
Trimmed Mean ( 3 / 27 )189.1558441558447.8622597349057324.0587121939075
Trimmed Mean ( 4 / 27 )190.1733333333337.7690857308368724.4782127423954
Trimmed Mean ( 5 / 27 )191.2191780821927.6686826457886424.9350751510368
Trimmed Mean ( 6 / 27 )192.2957746478877.5542676351516625.4552504538088
Trimmed Mean ( 7 / 27 )192.2957746478877.4270099412238125.8914120446432
Trimmed Mean ( 8 / 27 )194.6268656716427.276034396284126.7490304568981
Trimmed Mean ( 9 / 27 )195.4307692307697.2288141792322927.0349692750747
Trimmed Mean ( 10 / 27 )196.2222222222227.188146798767927.2980265589256
Trimmed Mean ( 11 / 27 )197.0327868852467.1405471623439627.593513831028
Trimmed Mean ( 12 / 27 )197.8644067796617.084629010864127.9286899111077
Trimmed Mean ( 13 / 27 )198.7192982456147.018671588584228.312950070043
Trimmed Mean ( 14 / 27 )198.7192982456146.9380308307904728.642031592554
Trimmed Mean ( 15 / 27 )200.6037735849066.8362741415442529.3440212360459
Trimmed Mean ( 16 / 27 )201.6470588235296.7110575145981730.046987138003
Trimmed Mean ( 17 / 27 )202.7142857142866.5663800483048130.8715432586968
Trimmed Mean ( 18 / 27 )203.8085106382986.4082248186554331.804207312605
Trimmed Mean ( 19 / 27 )204.9777777777786.2171552240301832.9697056598346
Trimmed Mean ( 20 / 27 )206.1627906976745.9969473807647634.3779555843599
Trimmed Mean ( 21 / 27 )206.9268292682935.9013630343587335.0642433050687
Trimmed Mean ( 22 / 27 )207.4615384615385.8631314669707635.3840843634921
Trimmed Mean ( 23 / 27 )207.9459459459465.8293996963442735.6719313785179
Trimmed Mean ( 24 / 27 )208.5142857142865.7720525496788836.124807236186
Trimmed Mean ( 25 / 27 )209.2121212121215.7046561219093536.6739233253025
Trimmed Mean ( 26 / 27 )2105.6077902803115837.4479054142396
Trimmed Mean ( 27 / 27 )210.8275862068975.4738673762704738.5152894132668
Median212
Midrange146.5
Midmean - Weighted Average at Xnp208.155555555556
Midmean - Weighted Average at X(n+1)p208.155555555556
Midmean - Empirical Distribution Function208.155555555556
Midmean - Empirical Distribution Function - Averaging208.155555555556
Midmean - Empirical Distribution Function - Interpolation209.931818181818
Midmean - Closest Observation208.155555555556
Midmean - True Basic - Statistics Graphics Toolkit208.155555555556
Midmean - MS Excel (old versions)208.155555555556
Number of observations83

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 186.084337349398 & 8.1503504107965 & 22.8314523879731 \tabularnewline
Geometric Mean & 163.823684646856 &  &  \tabularnewline
Harmonic Mean & 131.955614287802 &  &  \tabularnewline
Quadratic Mean & 200.186148311774 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 186.084337349398 & 8.12923105448815 & 22.8907674172529 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 186.10843373494 & 8.1154614580869 & 22.9325756392431 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 186.397590361446 & 8.05078538958027 & 23.1527212988053 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 186.493975903614 & 8.01406296820124 & 23.2708398528435 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 186.614457831325 & 7.98825230831606 & 23.3611121217407 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 186.614457831325 & 7.94176629430982 & 23.4978531117231 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 186.698795180723 & 7.92398381648263 & 23.5612287335029 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 189.590361445783 & 7.32740551807951 & 25.874146173293 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 190.024096385542 & 7.21882021092215 & 26.3234283211589 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 190.265060240964 & 7.17671006134008 & 26.5114597935194 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 190.530120481928 & 7.13089360827115 & 26.7189683297099 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 190.819277108434 & 7.081431903741 & 26.9464254831889 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 190.819277108434 & 7.0375998821041 & 27.1142549029631 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 190.987951807229 & 7.00907211908865 & 27.2486783645853 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 190.987951807229 & 6.9588964485284 & 27.4451492732899 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 191.566265060241 & 6.86217090933452 & 27.9162771652417 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 192.180722891566 & 6.70452640244042 & 28.6643248688846 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 192.397590361446 & 6.61006053763554 & 29.1067818919352 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 193.313253012048 & 6.46166679229128 & 29.9169330802804 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 198.614457831325 & 5.63931643895848 & 35.2195979745388 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 201.650602409639 & 5.20122371208224 & 38.7698383250103 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 202.710843373494 & 5.05452288769571 & 40.1048423120124 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 202.433734939759 & 5.02237698468375 & 40.3063600277521 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 201.855421686747 & 4.88375396149589 & 41.3320210801362 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 201.855421686747 & 4.80871638951162 & 41.9769862342095 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 202.481927710843 & 4.72348411846504 & 42.8670707114905 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 202.156626506024 & 4.68707785021093 & 43.1306312731559 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 187.061728395062 & 8.05401030541277 & 23.2259112295082 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 188.088607594937 & 7.96316148820211 & 23.61984092293 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 189.155844155844 & 7.86225973490573 & 24.0587121939075 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 190.173333333333 & 7.76908573083687 & 24.4782127423954 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 191.219178082192 & 7.66868264578864 & 24.9350751510368 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 192.295774647887 & 7.55426763515166 & 25.4552504538088 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 192.295774647887 & 7.42700994122381 & 25.8914120446432 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 194.626865671642 & 7.2760343962841 & 26.7490304568981 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 195.430769230769 & 7.22881417923229 & 27.0349692750747 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 196.222222222222 & 7.1881467987679 & 27.2980265589256 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 197.032786885246 & 7.14054716234396 & 27.593513831028 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 197.864406779661 & 7.0846290108641 & 27.9286899111077 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 198.719298245614 & 7.0186715885842 & 28.312950070043 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 198.719298245614 & 6.93803083079047 & 28.642031592554 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 200.603773584906 & 6.83627414154425 & 29.3440212360459 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 201.647058823529 & 6.71105751459817 & 30.046987138003 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 202.714285714286 & 6.56638004830481 & 30.8715432586968 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 203.808510638298 & 6.40822481865543 & 31.804207312605 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 204.977777777778 & 6.21715522403018 & 32.9697056598346 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 206.162790697674 & 5.99694738076476 & 34.3779555843599 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 206.926829268293 & 5.90136303435873 & 35.0642433050687 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 207.461538461538 & 5.86313146697076 & 35.3840843634921 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 207.945945945946 & 5.82939969634427 & 35.6719313785179 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 208.514285714286 & 5.77205254967888 & 36.124807236186 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 209.212121212121 & 5.70465612190935 & 36.6739233253025 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 210 & 5.60779028031158 & 37.4479054142396 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 210.827586206897 & 5.47386737627047 & 38.5152894132668 \tabularnewline
Median & 212 &  &  \tabularnewline
Midrange & 146.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 208.155555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 208.155555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 208.155555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 208.155555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 209.931818181818 &  &  \tabularnewline
Midmean - Closest Observation & 208.155555555556 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 208.155555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 208.155555555556 &  &  \tabularnewline
Number of observations & 83 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79008&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]186.084337349398[/C][C]8.1503504107965[/C][C]22.8314523879731[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]163.823684646856[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]131.955614287802[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]200.186148311774[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]186.084337349398[/C][C]8.12923105448815[/C][C]22.8907674172529[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]186.10843373494[/C][C]8.1154614580869[/C][C]22.9325756392431[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]186.397590361446[/C][C]8.05078538958027[/C][C]23.1527212988053[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]186.493975903614[/C][C]8.01406296820124[/C][C]23.2708398528435[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]186.614457831325[/C][C]7.98825230831606[/C][C]23.3611121217407[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]186.614457831325[/C][C]7.94176629430982[/C][C]23.4978531117231[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]186.698795180723[/C][C]7.92398381648263[/C][C]23.5612287335029[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]189.590361445783[/C][C]7.32740551807951[/C][C]25.874146173293[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]190.024096385542[/C][C]7.21882021092215[/C][C]26.3234283211589[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]190.265060240964[/C][C]7.17671006134008[/C][C]26.5114597935194[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]190.530120481928[/C][C]7.13089360827115[/C][C]26.7189683297099[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]190.819277108434[/C][C]7.081431903741[/C][C]26.9464254831889[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]190.819277108434[/C][C]7.0375998821041[/C][C]27.1142549029631[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]190.987951807229[/C][C]7.00907211908865[/C][C]27.2486783645853[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]190.987951807229[/C][C]6.9588964485284[/C][C]27.4451492732899[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]191.566265060241[/C][C]6.86217090933452[/C][C]27.9162771652417[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]192.180722891566[/C][C]6.70452640244042[/C][C]28.6643248688846[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]192.397590361446[/C][C]6.61006053763554[/C][C]29.1067818919352[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]193.313253012048[/C][C]6.46166679229128[/C][C]29.9169330802804[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]198.614457831325[/C][C]5.63931643895848[/C][C]35.2195979745388[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]201.650602409639[/C][C]5.20122371208224[/C][C]38.7698383250103[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]202.710843373494[/C][C]5.05452288769571[/C][C]40.1048423120124[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]202.433734939759[/C][C]5.02237698468375[/C][C]40.3063600277521[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]201.855421686747[/C][C]4.88375396149589[/C][C]41.3320210801362[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]201.855421686747[/C][C]4.80871638951162[/C][C]41.9769862342095[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]202.481927710843[/C][C]4.72348411846504[/C][C]42.8670707114905[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]202.156626506024[/C][C]4.68707785021093[/C][C]43.1306312731559[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]187.061728395062[/C][C]8.05401030541277[/C][C]23.2259112295082[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]188.088607594937[/C][C]7.96316148820211[/C][C]23.61984092293[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]189.155844155844[/C][C]7.86225973490573[/C][C]24.0587121939075[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]190.173333333333[/C][C]7.76908573083687[/C][C]24.4782127423954[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]191.219178082192[/C][C]7.66868264578864[/C][C]24.9350751510368[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]192.295774647887[/C][C]7.55426763515166[/C][C]25.4552504538088[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]192.295774647887[/C][C]7.42700994122381[/C][C]25.8914120446432[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]194.626865671642[/C][C]7.2760343962841[/C][C]26.7490304568981[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]195.430769230769[/C][C]7.22881417923229[/C][C]27.0349692750747[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]196.222222222222[/C][C]7.1881467987679[/C][C]27.2980265589256[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]197.032786885246[/C][C]7.14054716234396[/C][C]27.593513831028[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]197.864406779661[/C][C]7.0846290108641[/C][C]27.9286899111077[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]198.719298245614[/C][C]7.0186715885842[/C][C]28.312950070043[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]198.719298245614[/C][C]6.93803083079047[/C][C]28.642031592554[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]200.603773584906[/C][C]6.83627414154425[/C][C]29.3440212360459[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]201.647058823529[/C][C]6.71105751459817[/C][C]30.046987138003[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]202.714285714286[/C][C]6.56638004830481[/C][C]30.8715432586968[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]203.808510638298[/C][C]6.40822481865543[/C][C]31.804207312605[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]204.977777777778[/C][C]6.21715522403018[/C][C]32.9697056598346[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]206.162790697674[/C][C]5.99694738076476[/C][C]34.3779555843599[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]206.926829268293[/C][C]5.90136303435873[/C][C]35.0642433050687[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]207.461538461538[/C][C]5.86313146697076[/C][C]35.3840843634921[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]207.945945945946[/C][C]5.82939969634427[/C][C]35.6719313785179[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]208.514285714286[/C][C]5.77205254967888[/C][C]36.124807236186[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]209.212121212121[/C][C]5.70465612190935[/C][C]36.6739233253025[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]210[/C][C]5.60779028031158[/C][C]37.4479054142396[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]210.827586206897[/C][C]5.47386737627047[/C][C]38.5152894132668[/C][/ROW]
[ROW][C]Median[/C][C]212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]146.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]208.155555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]208.155555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]208.155555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]208.155555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]209.931818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]208.155555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]208.155555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]208.155555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]83[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79008&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79008&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean186.0843373493988.150350410796522.8314523879731
Geometric Mean163.823684646856
Harmonic Mean131.955614287802
Quadratic Mean200.186148311774
Winsorized Mean ( 1 / 27 )186.0843373493988.1292310544881522.8907674172529
Winsorized Mean ( 2 / 27 )186.108433734948.115461458086922.9325756392431
Winsorized Mean ( 3 / 27 )186.3975903614468.0507853895802723.1527212988053
Winsorized Mean ( 4 / 27 )186.4939759036148.0140629682012423.2708398528435
Winsorized Mean ( 5 / 27 )186.6144578313257.9882523083160623.3611121217407
Winsorized Mean ( 6 / 27 )186.6144578313257.9417662943098223.4978531117231
Winsorized Mean ( 7 / 27 )186.6987951807237.9239838164826323.5612287335029
Winsorized Mean ( 8 / 27 )189.5903614457837.3274055180795125.874146173293
Winsorized Mean ( 9 / 27 )190.0240963855427.2188202109221526.3234283211589
Winsorized Mean ( 10 / 27 )190.2650602409647.1767100613400826.5114597935194
Winsorized Mean ( 11 / 27 )190.5301204819287.1308936082711526.7189683297099
Winsorized Mean ( 12 / 27 )190.8192771084347.08143190374126.9464254831889
Winsorized Mean ( 13 / 27 )190.8192771084347.037599882104127.1142549029631
Winsorized Mean ( 14 / 27 )190.9879518072297.0090721190886527.2486783645853
Winsorized Mean ( 15 / 27 )190.9879518072296.958896448528427.4451492732899
Winsorized Mean ( 16 / 27 )191.5662650602416.8621709093345227.9162771652417
Winsorized Mean ( 17 / 27 )192.1807228915666.7045264024404228.6643248688846
Winsorized Mean ( 18 / 27 )192.3975903614466.6100605376355429.1067818919352
Winsorized Mean ( 19 / 27 )193.3132530120486.4616667922912829.9169330802804
Winsorized Mean ( 20 / 27 )198.6144578313255.6393164389584835.2195979745388
Winsorized Mean ( 21 / 27 )201.6506024096395.2012237120822438.7698383250103
Winsorized Mean ( 22 / 27 )202.7108433734945.0545228876957140.1048423120124
Winsorized Mean ( 23 / 27 )202.4337349397595.0223769846837540.3063600277521
Winsorized Mean ( 24 / 27 )201.8554216867474.8837539614958941.3320210801362
Winsorized Mean ( 25 / 27 )201.8554216867474.8087163895116241.9769862342095
Winsorized Mean ( 26 / 27 )202.4819277108434.7234841184650442.8670707114905
Winsorized Mean ( 27 / 27 )202.1566265060244.6870778502109343.1306312731559
Trimmed Mean ( 1 / 27 )187.0617283950628.0540103054127723.2259112295082
Trimmed Mean ( 2 / 27 )188.0886075949377.9631614882021123.61984092293
Trimmed Mean ( 3 / 27 )189.1558441558447.8622597349057324.0587121939075
Trimmed Mean ( 4 / 27 )190.1733333333337.7690857308368724.4782127423954
Trimmed Mean ( 5 / 27 )191.2191780821927.6686826457886424.9350751510368
Trimmed Mean ( 6 / 27 )192.2957746478877.5542676351516625.4552504538088
Trimmed Mean ( 7 / 27 )192.2957746478877.4270099412238125.8914120446432
Trimmed Mean ( 8 / 27 )194.6268656716427.276034396284126.7490304568981
Trimmed Mean ( 9 / 27 )195.4307692307697.2288141792322927.0349692750747
Trimmed Mean ( 10 / 27 )196.2222222222227.188146798767927.2980265589256
Trimmed Mean ( 11 / 27 )197.0327868852467.1405471623439627.593513831028
Trimmed Mean ( 12 / 27 )197.8644067796617.084629010864127.9286899111077
Trimmed Mean ( 13 / 27 )198.7192982456147.018671588584228.312950070043
Trimmed Mean ( 14 / 27 )198.7192982456146.9380308307904728.642031592554
Trimmed Mean ( 15 / 27 )200.6037735849066.8362741415442529.3440212360459
Trimmed Mean ( 16 / 27 )201.6470588235296.7110575145981730.046987138003
Trimmed Mean ( 17 / 27 )202.7142857142866.5663800483048130.8715432586968
Trimmed Mean ( 18 / 27 )203.8085106382986.4082248186554331.804207312605
Trimmed Mean ( 19 / 27 )204.9777777777786.2171552240301832.9697056598346
Trimmed Mean ( 20 / 27 )206.1627906976745.9969473807647634.3779555843599
Trimmed Mean ( 21 / 27 )206.9268292682935.9013630343587335.0642433050687
Trimmed Mean ( 22 / 27 )207.4615384615385.8631314669707635.3840843634921
Trimmed Mean ( 23 / 27 )207.9459459459465.8293996963442735.6719313785179
Trimmed Mean ( 24 / 27 )208.5142857142865.7720525496788836.124807236186
Trimmed Mean ( 25 / 27 )209.2121212121215.7046561219093536.6739233253025
Trimmed Mean ( 26 / 27 )2105.6077902803115837.4479054142396
Trimmed Mean ( 27 / 27 )210.8275862068975.4738673762704738.5152894132668
Median212
Midrange146.5
Midmean - Weighted Average at Xnp208.155555555556
Midmean - Weighted Average at X(n+1)p208.155555555556
Midmean - Empirical Distribution Function208.155555555556
Midmean - Empirical Distribution Function - Averaging208.155555555556
Midmean - Empirical Distribution Function - Interpolation209.931818181818
Midmean - Closest Observation208.155555555556
Midmean - True Basic - Statistics Graphics Toolkit208.155555555556
Midmean - MS Excel (old versions)208.155555555556
Number of observations83



Parameters (Session):
par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')